To determine the mass flow rate of a fluid flowing in a pipe and particularly of a liquid, use is frequently made of measuring devices which induce Coriolis forces in the fluid and derive therefrom a measurement signal representative of mass flow rate by means of a vibratory transducer and of control and evaluation electronics connected thereto.
Such Coriolis mass flowmeters have been known and in industrial use for a long time. EP-A 317 340, U.S. Pat. Nos. 5,398,554, 5,476,013, 5,531,126, 5,691,485, 5,705,754, 5,796,012, 5,945,609, and 5,979,246 as well as WO-A 99/51946, WO-A 99/40349, and WO-A 00/14485, for example, disclose Coriolis mass flowmeters with a vibratory transducer which responds to the mass flow rate of a fluid flowing in a pipe and comprises:                a single straight flow tube for conducting the fluid which vibrates in operation and communicates with the pipe via an inlet-side tube section and an outlet-side tube section;        an excitation system which in operation excites the flow tube into flexural vibrations in one tube plane; and        a sensor system for sensing inlet-side and outlet-side vibrations of the flow tube.        
As is well known, straight flow tubes excited into flexural vibrations according to a first form of natural vibrations cause Coriolis forces in the fluid passing therethrough. These, in turn, result in higher-order and/or lower-order coplanar flexural vibrations according to a second form of natural vibrations being superimposed on the excited flexural vibrations, so that the vibrations sensed on the inlet and outlet sides by means of the sensor system exhibit a measurable phase difference, which is also dependent on mass flow rate.
Usually, the flow tubes of such transducers, which are used in Coriolis mass flowmeters, for example, are excited in operation at an instantaneous resonance frequency of the first form of natural vibrations, particularly with the vibration amplitude maintained constant. Since this resonance frequency is also dependent on the instantaneous density of the fluid in particular, commercially available Coriolis mass flowmeters can also be used to measure the density of moving fluids.
One advantage of straight flow tubes is that they can be drained residue-free with a high degree of reliability in virtually any position of installation and particularly after a cleaning operation performed in-line. Furthermore, such flow tubes are much easier and, consequently, less expensive to manufacture than, for example, an omega-shaped or helically bent flow tube. A further advantage of a straight flow tube vibrating in the above-described manner over bent flow tubes is that in operation, virtually no torsional vibrations are caused in the connected pipe via the flow tube.
A significant disadvantage of such transducers consists in the fact that as a result of alternating lateral deflections of the vibrating single flow tube, transverse forces oscillating at the same frequency can act on the pipe, and that so far it has been possible to counterbalance these transverse forces only in a very limited manner and with a very large amount of technical complexity.
To improve the dynamic balance of the transducer and particularly reduce such transverse forces produced by the vibrating single flow tube and acting on the pipe on the inlet and outlet sides, the transducers disclosed in EP-A 317 340, U.S. Pat. Nos. 5,398,554, 5,531,126, 5,691,485, 5,796,012, and 5,979,246 as well as WO-A 00/14485 each comprise at least one single-part or multipart “antivibrator” which is fixed to the flow tube on the inlet and outlet sides. In operation, such antivibrators, which are implemented in the form of beams and particularly of tubes or as a physical pendulum aligned with the flow tube, vibrate out of phase with, particularly opposite in phase to, the respective flow tube, whereby the effect of the lateral transverse forces exerted by the flow tube and the antivibrator on the pipe can be minimized or even neutralized.
Such transducers with antivibrators have proved particularly effective in applications where the fluid to be measured has a substantially constant or only very slightly varying density, i.e., in applications where a resultant of transverse forces produced by the flow tube and counterforces produced by the antivibrator, which resultant acts on the connected pipe, can be readily preset to zero.
If used for fluids with widely varying densities, such as different fluids to be measured in succession, such a transducer, particularly one as disclosed in U.S. Pat. Nos. 5,531,126 or 5,969,265, has practically the same disadvantage, even though to a lesser degree, as a transducer without antivibrator, since the aforementioned resultants are also dependent on the density of the fluid and thus may differ considerably from zero. In other words, in operation, even an overall system composed of flow tube and antivibrator will be nonlocally deflected from an assigned static rest position as a result of density-dependent unbalances and associated transverse forces.
One possibility of reducing the density-dependent transverse forces is proposed, for example, in U.S. Pat. No. 5,979,246, in WO-A 99/40394, or in WO-A 00/14485. WO-A 00/14485, in particular, discloses a vibratory transducer for a fluid flowing in a pipe, said transducer comprising:                a flow tube vibrating in operation, for conducting the fluid, the flow tube communicating with the pipe via an inlet-side tube section and an outlet-side tube section, and the vibrating flow tube being, at least temporarily, laterally displaced from an assigned static rest position as a result of transverse forces produced therein, so that transverse impulses occur in the transducer;        an excitation system for driving the flow tube;        a sensor system for sensing vibrations of the flow tube; and        a first antivibrator, fixed to the inlet-side tube section, and a second antivibrator, fixed to the outlet-side tube section, for producing compensating vibrations, the compensating vibrations being such that the transverse impulses are compensated, so that a centroid of a vibration system formed by the flow tube, the excitation system, the sensor system, and the two cantilevers is kept in the same position.        
WO-A 99/40394 discloses a vibratory transducer for a fluid flowing in a pipe, said transducer comprising:                a flow tube vibrating in operation, for conducting the the fluid, the flow tube communicating with the pipe via an inlet-side tube section and an outlet-side tube section; and        an antivibrator fixed to the flow tube on the inlet side and outlet side, with transverse forces being produced in the vibrating flow tube and in the antivibrator;        a transducer case fixed to the inlet-side tube section and the outlet-side tube section;        an excitation system for driving the flow tube;        a sensing system for sensing vibrations of the flow tube;        a first cantilever, fixed to the inlet-side tube section and to the transducer case, for producing counterforces counteracting the transverse forces on the inlet side; and        a second cantilever, fixed to the outlet-side tube section and to the transducer case, for producing counterforces counteracting the transverse forces on the outlet side, the counterforces being such that the flow tube is held in an assigned static rest position despite the transverse forces produced.        
In the aforementioned transducers, including those described in U.S. Pat. No. 5,979,246, the problem of density-dependent unbalances is solved in principle by adapting an amplitude variation of the antivibrator to the flow-tube vibrations in advance and/or in operation, particularly by making the spring constants of the antivibrator amplitude-dependent, such that the forces produced by the flow tube and the antivibrator neutralize each other.
Another possibility of reducing density-dependent transverse forces is described, for example, in U.S. Pat. Nos. 5,287,754, 5,705,754, or 5,796,010. In the transducers disclosed therein, the transverse forces produced by the vibrating single flow tube, which oscillate at medium or high frequencies, are kept away from the pipe by means of an antivibrator that is very heavy in comparison with the flow tube, and by coupling the flow tube to the pipe relatively loosely, i.e., practically by means of a mechanical low-pass filter. A big disadvantage of such a transducer is, however, that the antivibrator mass required to achieve sufficient damping increases disproportionately with the nominal diameter of the flow tube. Use of such massive components, on the one hand, entails both increased assembly costs during manufacture and increased costs during installation of the measuring device in the pipe. On the other hand, it must always be ensured that a minimum natural frequency of the transducer, which decreases with increasing mass, is still far from the likewise very low natural frequencies of the connected pipe. Thus, use of such a transducer in industrial Coriolis mass flowmeters or Coriolis mass flowmeter-densimeters and particularly in meters for measuring liquids is limited to relatively small nominal diameters less than or equal to 10 mm.